In the data set below, what is the interquartile range?
50 52 52 52 52 58 74

The alternating series test is a technique for demonstrating convergence of an alternating series when its terms (1) become smaller in absolute value and (2) get closer to zero in the limit.

The Leibniz test, often referred to as the alternating series test, is a form of series test used to ascertain whether two alternate series are converging. Remember that the test cannot determine whether the series diverges. There are three conditions that must be met for the Alternating Series Test: The series needs to switch up. For large n, the words must become less significant. The nth term must equal zero. The second prerequisite appears superfluous. Another test must be used to demonstrate that a series diverges. The ideal plan is to use the Divergence Test to check for divergence in an alternating series first. You've reached your conclusion if the terms do not converge to zero.

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Answer:

According to the diagram,  is the polar angle (the "vertical" angle made with the positive z-axis) and  is the azimuthal angle (the "horizontal" angle made with the positive x-axis), so the convention used here is to take

Then for the spherical point (1, π/4, π/2), we have the corresponding Cartesian point (x, y, z), where

Step-by-step explanation:

Answer:

Below!

Step-by-step explanation:

Since there is a variable (x) on the L.H.S and a constant (-7) on the R.H.S, the line will be a vertical line intersecting the x-coordinate (-7).

~Graph attached

Determining the y-intercept of the line:

Since the line is a vertical line, it's y-intersept is undefined as it will never intersect the y-axis.

Determining the slope of the line:

To determine the slope of the line, pick any two points that is on the line.

Using the slope formula (y₂ - y₁/x₂ - x₁):

∴ Any number divided by 0 is undefined

Thus, the slope and the y-intercept are undefined.

So

line will be parallel to y axis

no y intercept as parallel to y axis means it will never intercept y axis

Graph attached

Answer:

f(4) = - 27

Step-by-step explanation:

substitute x = 4 into f(x) , that is

f(4) = - 2(4)² + 5 = - 2(16) + 5 = - 32 + 5 = - 27

Answer:

69

Step-by-step explanation:

Replace x with 4

-2(4)^2 +5

-8^2+5

64+5

69

The required explanation for log of base 10 is described.

The ability of logarithms to solve exponential problems is a large part of their strength. Examples of this include sound (measured in decibels), earthquakes (measured on the Richter scale), starlight brightness, and chemistry (pH balance, a measure of acidity and alkalinity).

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

The logarithm can be rewritten using the general rule. The common logarithm, which has a base of 10 always, is what you're dealing with when the log has no base.

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Answer: True statement

The formula for the phi correlation coefficient was derived from the formula for the Pearson correlation coefficient is True.

Phi correlation coefficient is a statistical coefficient that measures the strength of the association between two categorical variables.

The Phi correlation coefficient was derived from the formula for the Pearson correlation coefficient.

However, it is used to estimate the degree of association between two binary variables, while the Pearson correlation coefficient is used to estimate the strength of the association between two continuous variables.

The correlation coefficient is a statistical concept that measures the strength and direction of the relationship between two variables.

It ranges from -1 to +1, where -1 indicates a perfectly negative correlation, +1 indicates a perfectly positive correlation, and 0 indicates no correlation.

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Answer:

A

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = ax + x ← is in slope- intercept form

with slope m = a

• Parallel lines have equal slopes

then the slope of a line parallel to y = ax + c is

slope = a

The correct answer is option b. 15.77%. The annual discount rate, also known as the discount rate or the rate of return, can be calculated using the present value formula.

Given that a cash flow of £52 million in 5 years' time is currently valued at £25 million, we can use this information to solve for the discount rate.

The present value formula is given by PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

In this case, we have PV = £25 million, CF = £52 million, and n = 5. Substituting these values into the formula, we can solve for r:

£25 million = £52 million / (1 + r)^5.

Dividing both sides by £52 million and taking the fifth root, we have:

(1 + r)^5 = 25/52.

Taking the fifth root of both sides, we get:

1 + r = (25/52)^(1/5).

Subtracting 1 from both sides, we obtain:

r = (25/52)^(1/5) - 1.

Calculating this value, we find that r is approximately 0.1577, or 15.77%. Therefore, the annual discount rate is approximately 15.77%, corresponding to option b.

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The specific statistical methods and tests used may vary depending on the nature of the variables and the assumptions of the data.

If a psychologist wants to investigate the relationship between the students' test 2 scores and their blood pressure conduct a statistical analysis to determine the nature and strength of this relationship. Here's a general approach they can follow:

1.Hypothesis formulation: The psychologist needs to formulate a hypothesis about the relationship between the test 2 scores and blood pressure. For example, they might hypothesize that there is a positive correlation between the two variables, meaning that as test 2 scores increase, blood pressure also tends to increase.

2.Data collection: The psychologist samples 200 students and records their blood pressure during the final. They also note down their corresponding test 2 scores. It's important to ensure that the data collection process is standardized and accurate.

3.Data analysis: Once the data is collected, the psychologist can analyze it using statistical methods. They descriptive statistics, such as the mean, standard deviation, and range, for both the test 2 scores and blood pressure.

4.Correlation analysis: To examine the relationship between the variables, the psychologist can calculate the correlation coefficient. The most commonly used measure of correlation is the Pearson correlation coefficient (r), which ranges from -1 to +1. A positive r value indicates a positive correlation, a negative r value indicates a negative correlation, and a value close to zero suggests no or weak correlation.

5.Statistical significance testing: To determine if the observed relationship is statistically significant, the psychologist can perform a hypothesis test. The most common test for correlation is the t-test for correlation coefficients. The psychologist can calculate the p-value associated with the correlation coefficient and compare it to a predetermined significance level (e.g., 0.05). If the p-value is less than the significance level, the psychologist can reject the null hypothesis and conclude that there is a significant relationship between test 2 scores and blood pressure.

6.Effect size estimation: In addition to statistical significance, it's important to assess the practical significance or effect size of the relationship. The psychologist can calculate the coefficient of determination (r²2), which indicates the proportion of variance in one variable (blood pressure) that can be explained by the other variable (test 2 scores).

7.Interpretation: Based on the findings from the analysis, the psychologist can interpret the results and draw conclusions about the relationship between test 2 scores and blood pressure. They should consider the magnitude of the effect size, the statistical , and any limitations or potential confounding factors in their interpretation.

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The cost of each white led lights and colored led lights is $12 and $15 respectively.

Let

w + c = 27

3w + 2c = 66

From (1)

w = 27 - c

Substitute w = 27 - c into (2)

3w + 2c = 66

3(27 - c) + 2c = 66

81 - 3c + 2c = 66

- 3c + 2c = 66 - 81

- c = - 15

c = 15

Substitute c = 15

w + c = 27

w + 15 = 27

w = 27 - 15

w = 12

In conclusion, the task content can be solved using the concept of simultaneous equation.

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To find the volume, evaluate the double integral V = ∫[0 to 4] ∫[8-2y to 0] (cy²) dx dy, where c is a constant, over the region bounded by a = y² and x + 2y = 8.

To find the volume, we need to set up a double integral for the region bounded by the curves. The integral is evaluated over the limits of integration and the result will give the volume of the region under the surface.

To find the volume of the region under the surface z = cy² and above the area bounded by a = y² and x + 2y = 8, we need to set up a double integral.

First, let's find the limits of integration for x and y.

From the equation a = y², we can solve for y:

y = √a

From the equation x + 2y = 8, we can solve for x:

x = 8 - 2y

Now, we need to determine the bounds for integration.

For y, we can integrate from the lower limit to the upper limit of y², which is 0 to 4 (since 8 - 2y = 0 gives y = 4).

For x, we can integrate from the lower limit to the upper limit of 8 - 2y.

The volume V can be calculated using the following double integral:

V = ∬ D (cy²) dA

where D represents the region bounded by the given curves.

Therefore, the volume can be computed as:

V = ∫[0 to 4] ∫[8-2y to 0] (cy²) dx dy

Evaluating this integral will give the volume of the region under the surface z = cy² and above the area bounded by a = y² and x + 2y = 8.

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Answer:

it appears to be up

Step-by-step explanation:

Answer:

x = t(a+p)/4

Step-by-step explanation

Given the expression

​a=4x/t - p

We are to make x the subject of the formula

a=4x/t - p

Add p to both sides

a+p = 4x/t - p+p

a+p = 4x/t

Cross multiply

t(a+p) = 4x

Rearrange

4x = t(a+p)

Divide both sides by 4

4x/4 = t(a+p)/4

x = t(a+p)/4

Answer: 96 ft²

Step-by-step explanation:

This figure can be divided into two rectangles:

Find the area of both rectangles:

Add them together to find the total area of the figure:

84 + 12 = 96 ft²

Answer:

i think it's a quadrilateral it's a rhombus.

Step-by-step explanation:

hope this helps

W is a subset of span(w), and span(w) is closed under vector addition, scalar multiplication, and contains the zero vector, we know that w must also have these properties. Therefore, w is a subspace of v.

To show that a subset w of a vector space v is a subspace of v if and only if span(w) = w, we need to prove both directions of the equivalence:

First, we'll assume that w is a subspace of v. In this case, we know that w is closed under vector addition and scalar multiplication, and that it contains the zero vector.

To show that span(w) = w, we need to prove two things:

span(w) is a subset of w: This is true by definition of span(w) - every vector in span(w) can be written as a linear combination of vectors in w, so it must be in w as well.

w is a subset of span(w): This is also true, because every vector in w is itself a linear combination of vectors in w (namely, itself with a coefficient of 1), so it is also in span(w).

Therefore, we have shown that span(w) = w.

Next, we'll assume that span(w) = w. In this case, we know that every vector in w can be written as a linear combination of vectors in w. We need to show that w is closed under vector addition and scalar multiplication, and that it contains the zero vector.

Let u, v be two vectors in w, and let c be a scalar. Then we can write:

\(u = a1w1 + a2w2 + ... + anwn\)

\(v = b1w1 + b2w2 + ... + bnwn\)

where w1, w2, ...,\(wn\) are vectors in w, and a1, a2, ..., an, b1, b2, ...,\(bn\)are scalars.

Then, we have:

\(u + v = (a1+b1)*w1 + (a2+b2)*w2 + ... + (an+bn)*wn\)

which is a linear combination of vectors in w, so u + v is in w.

Also, we have:

\(cu = c(a1w1 + a2w2 + ... + anwn) = (ca1)w1 + (ca2)w2 + ... + (can)*wn\)

which is also a linear combination of vectors in w, so c*u is in w.

Finally, since w is a subset of span(w), and span(w) is closed under vector addition, scalar multiplication, and contains the zero vector, we know that w must also have these properties. Therefore, w is a subspace of v.

Therefore, we have shown both directions of the equivalence, and proved that a subset w of a vector space v is a subspace of v if and only if span(w) = w.

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Answer:

I think the one you have picked (miles per gallon, gallons in tank)

Step-by-step explanation:

This one really doesn't make sense without context and there is no way to determine miles per gallon and gallons per tank on a graph that is a function. (Function=Every input has only one output)

Answer:

a=1

b=-6

Step-by-step explanation:

Instead of x, we plug in -5.

a(4-(-5))=-3(-5)+b

Then, we simplify.

a(9)=15+b

At last, we look at the possible answers and see what could possibly work.

a=1

b=-6

base area = pi r2

9 pi = pi r2

9=r2

r= root 9

radius = 3cm

vol = 1/3pir2h

1/3pir2h=12pi

height =4cm

slant height = root ( r2+h2)

9+16=25 root 25 =5

slant height = 5cm

surface area = pir(r+(rooth2+r2))

=75.4cm2

Answer:

Length = 107cm, Width = 20cm

Step-by-step explanation:

Length = L

Width = W

Then, from first statement:

L = 5W + 7. (eqn1)

From second statement:

2(L + W) = 254. (eqn2)

solving the equations:

substitute (eqn1) into (eqn2) for L.

2(5W + 7 + W) = 254

6W + 7 = 127

6W = 127 - 7

6W = 120

W = 120/6

W = 20.

from (eqn1);

L = 5W + 7

L = 5(20) + 7

L = 107

Answer:777

Step-by-step explanation: I do not care

There are 333 pages are in my book.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are more than 200 pages but fewer than 800 in my book.

And, All the digits of my number are the same and the number is divisible by 9.

Now,

Let a number with three same digit = xxx

So, We get;

200 < xxx < 800

Since, the number is divisible by 9.

So, By the rule of the number divide by 9, we get;

x + x + x = 9k

3x = 9k

for k = 1;

x = 3

Thus, Number of pages = 333

Therefore,  

There are 333 pages are in my book.

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Answer: 55 degrees

Step-by-step explanation:

a+90+35=180 ==> a straight line measures 180 degrees and the angles a, a right angle, and 35 lie on that line. A 180 degree angle is called a straight angle. Also, if there is a tiny box in between an angle, that means that the angle is a right angle.

a+125=180

a+125-125=180-125

a=180-125

a=55 degrees

The maximum possible number of elements in set B is 62.

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.

The universal set is A consisting of the primary one hundred positive integers.

Now, Set B is a subset of A.

Set B might be made up of the first 62 positive numbers, for example.

Only then is 123 the largest number that can be formed by adding all the components of set B.

Set B contains 62 items altogether.

Additionally, we can carefully swap out one or more pieces from set B and add them to its complement.

In the majority of these cases, set B may have 62 elements.

Therefore, we get the number of elements in set B will be 62.

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Answer:

17 w  +  35

Step-by-step explanation:

You get this answer by using PEMDAS.

Answer:

( 6 + s ) ÷ 4

Step-by-step explanation:

MUST KNOW WHAT S IS TO SOLVE EQUATION

Answer:

option c

Step-by-step explanation:

(4 - 2i) + (12 + 7i)

multiply the brackets first

4 - 2i + 12 + 7i

combine like terms

16 + 5i

Answer:

O C. 16+5i

Step-by-step explanation:

=(4+12) + (7i-2i)

=16+5i

Solution

First convert the feet to inches:

8 feet= 96 in.; 4 feet=48 in.

Make an equation for each one:

Type A: h=36+15x